Answer
a) The equation of the linear relationship is $y = -1600x + 20700$.
b) The value of the automobile by 2012 is $11,100.
See Graph I for the details
Work Step by Step
a) Since the relationship between the value of the automobile and the number of years past 2006 is assumed to be linear (given), by referring to Graph I, the equation of the linear relationship is
$\frac{y - 14300}{x - 4}$ = $\frac{17500 - 14300}{2 - 4}$
$\frac{y - 14300}{x - 4}$ = $-\frac{3200}{2}$
$2(y - 14300) = -3200(x - 4)$
$2y - 28600 = -3200x + 12800$
$2y = -3200x + 41400$
$y = -1600x + 20700$
The equation of the linear relationship is $y = -1600x + 20700$
b) For the value of the automobile by 2012 (6 years past 2006), it will be
$y = -1600(6)+ 20700$
$y = -9600 + 20700$
$y = 11100$
The value of the automobile by 2012 is $11,100.
See Graph I for the details.
